Method for optimum miscible flooding of reservoirs using a model to determine input profile



o PRODUCTION WELL Aug. 1, 1967 J. P. HELLER 3,333,631

METHOD FOR OPTIMUM MISCIBLE FLOODING OF RESERVOIRS USING A MODEL TODETERMINE INPUT PROFILE Filed Dec. 5, 1964 FIG. I

PRIOR ART FLOODING FORMATION w JOHN P. HELLER I NVEN TOR.

INJECTION WELL u v T 5 '2 FL ID MO EMEN 7 BY a M ATTORNEY United StatesPatent METHOD FOR OPTIMUM MISCIBLE FLOODING 0F RESERVOIRS USING A MODELT0 DETER- MINE INPUT PROFILE John P. Heller, Dallas, Tex., assignor toMobil Oil 5 Corporation, a corporation of New York Filed Dec. 3, 1964,Ser. No. 415,640 6 Claims. (Cl. 166-4) ABSTRACT OF THE DISCLOSURE 10This specification describes:

A model is provided representative of a formation, with its injectionand production wells, in which miscible flooding is to be used forpetroleum recovery. However, the wells employed in the model forinjection and production purposes are functionally reversed from thosein the formation. Additionally, in the model, the fluids representativeof the miscible displacing fluid and the petroleum are also reversed;the former fluid being produced, and the latter fluid being injected,through the wells of the model. Operating this model produces, whenbreakthrough of the represented displacing fluid occurs, a flood frontprofile which is the input profile for optimum petroleum recovery in theformation. This input profile is established in the miscible displacingfluid which is injected into the formation in practicing the method forpetroleum recovery by which petroleum is produced with optimum recovery.

This invention relates to the recovery of petroleum from a subterraneanreservoir and relates more particularly to such recovery by the miscibleflooding of the reservoir. In another aspect, the present invention alsorelates to a method for determining the input profile of a flood frontto be established at an injection well for effecting optimum miscibleflooding of the reservoir.

Petroleum is recovered from subterranean reservoirs by various methods.Among these methods is the flooding of the formation comprising thereservoir with a fluid miscible with the native petroleum. The fluidmiscibly' displaces the petroleum from the formation and moves it beforea flood front toward a a production well. The method of miscibleflooding may be employed initially for the production of petroleum orwhere further amounts of petroleum are believed to be recoverable fromthe formation after another procedure has been practiced.

In the method of miscible flooding of the formation for the recovery ofpetroleum, the successive shapes of the advancing front of thedisplacing fluid in the formation surrounding each injection well aredetermined by various factors. Among these factors are included theinhomogeneities of the formation, the number and relative position ofthe injection nad production wells, the configuration of the grossboundaries of the reservoir, and the fluid properties of the displacedfluid and the displacing fluid. The successive shapes of the areathrough which the displacement or flood front passes are termed thesweep patterns and the ratio of the area within the sweep pattern to thetotal area at some stage in a displacement program is termed the sweepeficiency at that stage of the flood. Obviously, for economic operadons,a maximum sweep efliciency is required commensurate with the number ofinjection and production wells. Usually, the injection and productionwells are arranged in regular and uniform geometric patterns. Especiallynear the edges of a delevolped field, however, the placement of thewells may depart significantly from these patterns. In many instances,high areal sweep efliciencies may be obtained with these well patterns,but for various reasons still higher efliciencies are desired.

One criterion which effects the sweep efliciencies is the shape of theflood front surrounding each injection well. This front shape isdetermined by various factors which include various geometricalcharacteristics. These characteristics arethe variations in theformation and include inhomogeneities of the porosity, permeability, andnative fluid saturation and surface properties of the formation rocksmatrix. These may be called the formation inhomogeneities, and mayinclude random variations of the matrix from microscopic pore-sizeddimensions up to large scale trends in the rock properties over thegross dimensions of the formation. They may also be highly orderedvariations in the rock parameters, such as a strongly layered structure.Among the geometrical characteristics involved in the determination ofthe shape of the displacement front are the relative positions of theinjection and production wells and the shape of the gross formationboundaries.

In addition to these geometrical factors, the shape of the flood frontmay also be under the influence of the fluid properties. This ispossible if there exists a difference in mobility and density betweenthe displaced fluid and the displacing fluid. Variations in frontalshape may 'then themselves effect changes in the velocity of fluidmovement. Whenever the mobility of the displacing fluid is higher thanthat of the displaced fluid, the front shape becomes unstable anddevelops extensions or fingers. These fingers may continue to developduring the displacement flooding and will break through into theproduction well wit-h the resultant dilution of the produced petroleumwith displacing fluid. As one result of such breakthrough effects, thelifetime of the field during which petroleum may be producedeconomically is decreased.

The flood fronts surrounding injection well just after start of theinjection program are relatively smooth in their input profile andreflect the shape of the input boundaries, which are usually thecylindrical bores of the injection wells. This is the case even infloods in which the ratio of fluid mobility of the displaced phase tothat of the displacing phase is greater than unity, i.e., an adversemobility ratio. As the miscible flooding proceeds, the flood frontdevelops irregularities corresponding to the effects of the geometricalcharacteristics mentioned above. These are further amplified by thepositive feedback or instability engendered by the adverse mobilityratio, and develop further into fingers which reduce the sweepefficiency.

A process evolved for remedying the effects of the fingering in theabove-mentioned situations for recovering petroleum is described in acopending application, Ser. No. 309,123, filed Sept. 16, 1963, by thepresent applicant, and now US. Patent No. 3,286,768. In this process,within the formation containing petroleum, one or more instabilityfingers of the displacing fluid are intentionally created and orientedin directions from the injection well to a production well in which theflow is ordinarily the slowest. These instability fingers produce aninput profile in the flood front of the displacing fluid of a shapewhich counteracts the above undesired effects. Various methods forcreating selectively oriented instability fingering of the displacingfluid to establish a desired input profile in the flood front may beemployed. Preferably, an instability finger is created by injecting thedisplacing fluid from the injection well into the formation through adirectionally oriented void created Within the formation from the wallof the well. For example, the injection well is first perforatedemploying conventional gun perforating means to create a directionallyoriented void. Through this void is injected'the displacing fluid tocreate one or more instability fingers which establish the desired inputprofile in the flood front of the displacing fluid. The influence ofthese intentionally produced instability fingers "in the input profileon the shape of the flood front is maintained as the front moves awayfrom the injection well by continued control of flow of the injecteddisplacing fluid. Further, an optimum input profile if established atthe injection Well would provide the flood front of displacing fluidwith truly radial flow conditions as it approaches the production well.These radial flow conditions would produce increased sweep efliciencyand extend to a maximum the time of recovering petroleum from theproduction well before unduly large amounts of displacing fluid arrive.

The input profile of the flood front may be created initially adjacentthe injection well with a shape to reflect application of instabilityfingers generally aligned with the direction of the slowest flow ofdisplacing fluid. However, it would be preferred that a more exactmethod be employed for determining the optimum input profile of theflood front of the displacing fluid immediately adjacent the injectionwell for effecting optimum recovery of petroleum by the miscibleflooding procedure.

It is the principal purpose and object of the present invention toprovide a method for recovering petroleum from subterranean reservoirsby miscible flooding procedures employing the determination of theoptimum input profile to be established for the displacement flood frontat the injection well and establishing the optimum input profile in theflood front of the displacing fluid for effecting the miscible floodingof the formation for the improved recovery of petroleum.

The objects of this invention will be apparent when read in conjunctionwith the following description, the appended claims, and the attacheddrawings, wherein:

FIGURE 1 is a plan view of a petroleum reservoir provided with a -spotwell pattern in the producing formation in which one quadrant isillustrated with the positions and shapes of successive flood fronts ofthe displacing fluid injected into the centrally disposed injection wellin accordance with prior art miscible flooding procedures;

FIGURE 2 is a plan view of a petroleum reservoir model ofthe formationshown in FIGURE 1; and

FIGURE 3 is the formation in plan view including the same well patternas in FIGURE 1 but illustrating the positions and shapes of successiveflood fronts in the displacing fluid resulting from employing thepresent invention.

The present invention is based on the modeling of the Darcy flow offluids through porous materials, and on the principle of reversibilityin such flows.

The operation of reservoir models representing a Darcy flow system inthe actual operation of the formation is dependent upon certain knownprinciples of dimensional analysis. Various types of hydrodynamic,potentiometric and electrical analog models have been employed inmiscible flooding studies of reservoirs and for other purposes. Examplesof these models are the conductive cloth models, gelatin models,electrolytic models, sand bed models, and the electrical analog modelsemploying circuits of resistances and capacitances.

In the hydrodynamic model, fluids are flowed through permeable porousmedia, or within a narrow gap between two flat plates, to represent theDarcy flow system of the formation in a reservoir study. In thepotentiometric or electrical analog models, the fluid flows and thepermeable porous media of the prototype formation are representedfunctionally through analogy of the flow of electricity to the Darcyflow system. For example, the use of models in methods for increasingthe recovery of petroleum from formations is described in United StatesPatents 2,867,277 and 2,994,372. The first-identified patent illustratesHele- Shaw models, which are hydrodynamic models. For the results of themodels representing Darcy flow systems to be transferred practicably tothe operation of the formation requires that the two be substantiallysimilar in their Darcy 'flow systems. For this purpose, the followingconditions of similarity must be present in both the model and theformation.

Geometrical similarity 7 There must be a geometrical similarity of bothsystems in the microscopic boundary shapes, both internal and external,and in the transitional zone shape at some reference time of thedisplacement front. In addition, all known inhomogeneities, includingporosity and permeability, should also be scaled such that these valuesat any point in the model are proportional to their respective values inthe formation.

Dimensionless numbers The values of certain dimensionless numbers, whichare descriptive of the relative strength of the various naturalprocesses shaping the displacement and flow processes, must besubstantially the same in both model and formations. These dimensionlessnumbers may vary in their precise form and some degree of choice intheir selection exists. However, a complete set is as follows:

(A) The mobility ratio M must be the same in both systems. M is in thiscase, where miscible displacement is effected, the ratio of theviscosity of the displaced fluid to the viscosity of the displacingfluid.

(B) The Gravity Override Number must be the same. This function isdefined as V wherein:

g is the acceleration of gravity;

k is the formation permeability;

A is the density difference between the displaced and the displacingfluids; 7

,u. is their mean viscosity; and

W is the Darcy velocity at some characteristic point in the flow system.

This insures that in both systems the effect of gravity on theorientation of the isodensity surfaces will be the same. The scaling ofthis number is only unnecessary when the overriding effect isnegligible.

(C) The Transverse Dispersion Number must be the same in both systems.The function is defined as wherein:

D,, is the coeflicient of transverse dispersion;

A is a characteristic macroscopic length in the flow length;

and

W is again the Darcy velocity at some characteristic point in the flowsystem.

The coefiicient D, is a function of the molecular diffusion coeflicientbetween the fluids used, and also depends on the internal rock geometryand the flow rate.

(D) The Longitudinal Dispersion Number must be the same in both systems.This function is defined as wherein:

A and W have the above definitions; and

D is the coefficient of longitudinal dispersion of the flow system.

the scalar (concentration) field. Obviously, if the transition zonebetween the fluids were of zero thickness, then the front would beinfinitely sharp since all of the isoconcentration curves would mergeinto one. In the practical case, however, to be considered, the front isgraded and therefore the transition zone occupies an appreciable area.

The time evolution of the shape of the displacement front is dependenton the above set forth dimensionless numbers and this dependence is oftwo kinds. These kinds are the dispersive changes and the Darcy-changes.The dispersive changes occur due to the process of diffusion and itsinteraction with the microscopic fluid velocity variations in theformation. By maintaining the two dispersion numbers, the TransverseDispersion Number, and the Longitudinal Dispersion Number as well as theconcentration ga-rdient small in magnitude, the dispersive changes willbe negligible in comparison with those frontal shape changes dependentupon the Darcy-changes. These Darcychanges may be classified themselvesas those which relate to the shape of the external boundary and thosewhich occur as a result of the feedback situation engendered byviscosity and density differences between the displaced and thedisplacing fluids.

Referring now to FIGURE 1, the Darcy-changes and their results will bedescribed in reference to a petroleum reservoir consisting of formationhaving uniform isotropic geometrical characteristics and in which aconventional miscible flooding procedure is practiced. In the formation10', injection well 11 and production wells 12, 13, 14, and 15 areprovided in a 5-spot uniform and regular geometric well pattern. Theincreased fingering of successive fronts created by injecting adisplacing fluid, such as propane or liquefied petroleum gases, denotedhereinafter as LPG, into the injection Well 11 clearly displays in theupper right quadrant of formation 10 the response to the existinggeometrical characteristics. These sweep patterns behind these frontsare typical of a 5-spot displacement with a moderately adverse mobilityratio and with the flood front graded sufliciently to suppress thedevelopment of high wave number instability fingers. They do show thegrowth of the dominant instability pattern of wave number 4, which isinitiated by the fourfold symmetry of the 5-spot pattern. The front 16has a circular shape representative of radial flow conditions from theinjection well 11. The degree to which the nosing of each of thesuccessive fronts 17, 18, 19, and 20 protrudes, as well as rate at whichthe shape change by fingering occurs, is dependent on the viscosityratio of the displacing and the displaced fluids. The front 20illustrates breakthrough of the displacing fluid at a time when asubstantial amount of petroleum or crude oil remains within the confinesof the S-spot symmetry unit. Both of these Darcychanges in frontal shapeare reversible in time. It is on this time reversibility that thepresent method is based, and by which a model is employed, wherein thepositive time direction in the formation is represented by negative timedirection in the model.

Referring now to FIGURE 2, the method of the present invention will bedescribed wherein a model is employed of the formation 10 which :byprior art flooding procedures produces the undesired fingering effectsin the successive fronts shown in FIGURE 1. FIGURE 2 represents a model21 of the formation 10 portrayed in FIGURE 1. This model 21 may beconstructed in any conventional manner. It also will be helpful to matchdispersion numbers with the reservoir, however.

In the model employed, whether of the hydrodynamic or any other knowntypes, it is to be understood that tain mobility ratio relationship totheir counterparts in the formation.

The model construction described in the aforementioned United StatesPatent 2,867,277 for a hydrodynamic model in providing the model 21 isemployed for illustrative and descriptive purposes. The model 21 isarranged to have functionally the same Darcy flow system as theformation of the formation 10. However, the production well 13 in theformation 10 is represented by injection well 22 in the model 21, andthe injection well 11 in the formation 10 is represented by a productionwell 23 in the model 21.

The model 21 is now operated with displaced and displacing fluids havinga mobility ratio M equal to the reciprocal of the ratio of the viscosityof the displaced fluid to the viscosity of the displacing fluidassociated with the prototype formation 10.

In a particular embodiment the displacing and displaced fluids employedin the model 21 may be the displaced and displacing fluids,respectively, associated with the formation 10. More particularly, andas one example, the native petroleum of the formation 10 is introducedvia the injection well 22 into the model 21 and the displacing fluidinjected into the formation 10, such as LPG, is the displaced fluidnative to the model which fluid is produced from the production well 23.However, other fluid flows of displacing and displaced fluids asfunctionally employed in the model 21 may be used representing thedisplacing and displaced fluids associated with the formation 10 butwith the reciprocal mobility ratio relationship.

Introduction of the displacing fluid through the injection well 22 intothe model 21 results in successive fronts 24, 25, 26, 27 and 28 beingcreated in progression toward the production well 23 from whichdisplaced fluid is produced. Obviously, these fronts 24 to 28,inclusive, are successively formed positive in time direction relativeto the model 21 but negative in time direction when compared to theformation 10 of FIGURE 1. It is apparent that whereas the displacementfronts 16 to 20, inclusive, are unstable and result in the fourth-orderfingering into the formation 10 of FIGURE 1, the fronts 24 to 28,inclusive, are superst-able in the model 21 portrayed in FIGURE 2. Thus,the fronts 24, 25, and 26 adjacent the injection well 22 correspond toradial flow conditions with flow velocity independent of azimuth angleand thusly are circular. Each of the successive fronts 27 and 28 towardthe production well 23 undergoes transition from a circular shape as theinfluence of the production well 23 overcomes eventually thesuperstability resulting from the favorable mobility ratio. Ofparticular notice is the shape or the profile of the front 28immediately adjacent the production well 23 in the model 21. Since fluidmovements in the model 21 in FIGURE 2 are negative in time directionrelative to their counterparts in the formation 10 shown in FIGURE 1,the profile of the flood front 28 adjacent the production well 23 inFIGURE 2 is of the desired shape for the injection front to beestablished by any suit-able means at the injection well 11 in theformation 10 shown in FIGURES 1 and 3. Obviously, the sequence of floodfront configurations in the model 21 in FIGURE 2 will be the same asthat desired forthe formation 10 except for a reversal of their order intime and direction of movement. The method of determining the inputprofile has many uses besides in the following described method forrecovering petroleum. For example, such input profiles may be determinedin studies for the best placement of wells in a reservoir.

Referring now to FIGURE 3, there is shown the formation 10 with theinjection well 11 and production well 13 as priorly described withreference to FIGURE 1, and wherein the shape of the flood front 28obtained with the model 21 of FIGURE 2 is established as the inputprofile, adjacent the injection well 11, in a flood front 29 of injecteddisplacing fluid. The displacing fluid may be any 'jection well 11.

fluid employed for the miscible displacement of petroleum, and oneexample is LPG. It will be seen that the continued injection of thedisplacing fluid into the injection well 11 at the flow conditionsemployed for establishing the desired input profile displaces thepetroleum toward, and to be produced from, the production well 13 on theformation 10 shown in FIGURE 3. This action will produce successivedisplacement fronts 30, 31, 32, and 33 having configurations exactly asthey appear in the model 21 of FIGURE 2 in the fronts 27, 26, 25, and24, respectively. The only difference between these successivedisplacement fronts in FIGURES 2 and 3 is that they are reversed intheir order in time and direction of movement. Thus, the successivefronts 31, 32, and 33 have :a circular configuration representing radialfiow conditions for some distance from the production well 33. Theseradial flow conditions produce a substantial increase in the sweepefliciency of the displacement fronts in the miscible floodingprocedure. As one result, a greater amount of petroleum is produced fromthe formation 10 than could be obtained in the formation 10 byconventional methods :as represented in FIGURE 1.

As previously mentioned, the process of dispersion causes the frontalthickness to become progressively greater in the positive direction oftiime in both the model 21 of FIGURE 2 and the formation 10 of FIG- URE3. This, of course, limits the time reversal modeling method of thisinvention to situations in which the dispersive effects are small.However, it will be seen that these situations are precisely those towhich modeling is limited by other considerations as well. Additionally,it is desired to reduce to a great degree the growth of instabilityfingers in the displacement fronts 29 to 33 of high-wave numbers in theunstable displacement front configuration of the formation 10 shown inFIGURE 3. The formation of the high-wave number fingers in thedisplacement fronts may be restricted where the front has a relativelybroad transition zone, that is, one with a large grading distance. Inthis case, the growth rates of the high-wave number fingers are muchreduced, while the growth rates of the lower order wave perturbations,such as the fourth (which is dominant when a -spot geometric wellpattern is employed) are relatively unaffected. By employment of largegrading distances in the model 21, as well as in the formation 10, theundesired effects of dispersion and of the formation of highwave numberfingerings are avoided. Generally, an appropriate grading length willdepend upon the value of the mobility ratio. Preferably, the higher the,mobility ratio M, the greater will be the required grading length.However, this is true in all models employed in miscible displacementflooding procedures.

Thus, in summary, the shape of the flood front 28 in the model 21 isdetermined from the last of the successive flood fronts 24 to 28 as hasbeen described. The shape of the flood front 28 may be recorded in anysuitable manner for future use, if desired. This shape is utilized asthe input profile of the flood front 29 to be established adjacent theinjection well 11 of the formation 10. The input profile of the floodfront 29 can be established by the injection of the displacing fluid inany suitable manner from the injection well 11. For example, theselective formation of instability fingers by directional perforationmay be used. Continuing injection of the miscible displacing fluid, suchas LPG, into the injection well 11 produces the successive fronts 30,31, 32, and 33 until the breakthrough occurs into the production well13. The displaced petroleum is produced or recovered from the productionwell 13 under radial flow conditions which extend therefrom asubstantial distance toward the in- Obviously, by the foregoing steps,greater sweep efliciency by the displacing fluid is obtained along withan extension of the time over which petroleum can be pro- G duced fromthe production well 13 without undue collateral production of thedisplacing fluid. These results mean an improved production of petroleumthrough utilization of the method of this invention.

From the foregoing it will be apparent that a method is disclosed whichaccomplishes all of the stated objects of this invent-ion. Variousmodifications of the disclosed method may be made by those skilled inthe art without departing from the spirit of this invention. For thisand other reasons, the present description is intended to beillustrative of this invention, and only the appended claims are to beconsidered as limitative of the invention.

What I claim is:

1. In a method for the production of petroleum from a formationpenetrated by injection well means and production well means by theinjection of a miscible displacing fluid into said formation throughsaid injection well means and displacement of said petroleum by saiddisplacing fluid in the direction of said production well means, thesteps comprising:

(a) providing a reservoir model having functionally the same Darcy flowsystem including geometrical similarity and dimensionless numbers, andthe same arrangement of well means for injection and production purposesas the formation,

(b) operating the model with the well means employed in the formationfor injection and production purposes functionally interchanged in thewell means of the model for production and injection purposes,respectively, and with the ratio of the viscosity of the miscibledisplacing fluid to the viscosity of the displaced fluid as functionallyemployed in the model being the reciprocal of the ratio of the viscosityof the miscible displacing fluid to be injected into the formation tothe viscosity of the native petroleum to be displaceably producedtherefrom, and operating said model until the shape of the flood frontin the model is established at the time representative of the miscibledisplacing fluid approaching breakthrough into the production wellmeans,

(c) injecting the miscible displacing fluid via the injection well meansinto the formation to form therein a flood front,

((1) establishing in the formation adjacent the injection well means inthe flood front through flow conditions of the injected displacing fluidan input profile with a shape substantially the same as the flood frontshape at the time representative of the miscible displacing fluidapproaching breakthrough into the production well means in the model,

(e) continuing at the same flow conditions the miscible displacing fluidinjection into the injection well means of the formation to move theflood front toward the production well means, and

(f) producing petroleum from the production well means in the formation.

2. A method for determining the input profile of a flood front shape tobe established adjacent injection Well means in a formation for theoptimum production of petroleum therefrom by a miscible floodingprocedure employing the injection of a miscible displacing fluid intosaid formation through injection well means for displacement ofpetroleum in the direction of production well means from which petroleumis recovered, the steps comprising: V

(a) providing a reservoir model having functionally the same Darcy flowsystem including geometrical similarity and dimensionless numbers, andthe same arrangement of well means for injection and production purposesas the formation, 7

(b) operating the model with the well means employed in the formationfor injection and production purposes functionally interchanged in thewell means of the model for production and injection purposes,

respectively, and with the ratio of the viscosity of the miscibledisplacing fluid to the viscosity of the displaced fluid 'asfunctionally employed in the model being the recipurocal of the ratio ofthe viscosity of the miscible displacing fluid to be injected into theformation to the viscosity of the native petroleum to be displaceablyproduced therefrom, and

(c) operating said model until the shape of the flood front in the modelis established at the time representative of the miscible displacingfluid approaching breakthrough into the production well means.

3. In a method for the production of petroleum from a formationpenetrated by injection well means and production well means by theinjection of a miscible displacing fluid into said formation throughsaid injection well means and displacement of said petroleum by saiddisplacing fluid in the direction of said production well means, thesteps comprising:

(a) providing a hydrodynamic reservoir model having functionally thesame Darcy flow system including geometrical similarity anddimensionless numbers, and the same arrangement of well means forinjection and production purposes as the formation,

(b) operating the model with the well means employed in the formationfor injection and production purposes functionally interchanged in thewell means of the model for production and injection purposes,respectively, and with a displacing fluid injected into the injectionwell means to move a displaced fluid toward the production well means,and where the ratio of the viscosity of said displacing fluid to theviscosity of said displaced fluid employed in the model is thereciprocal of they ratio of the viscosity of the miscible displacingfluid to be injected into the formation to the viscosity of the nativepetroleum to be displaceably produced therefrom, and operating saidmodel until the shape of the flood front in the model is established atthe time representative of the miscible displacing fluid approachingbreakthrough into the production well means,

(c) injecting the miscible displacing fluid via the injection well meansinto the formation to form therein a flood front,

(d) establishing in the formation adjacent the injection well means inthe flood front through flow conditions of the injected displacing fluidan input profile with a shape substantially the same as the flood frontshape at the time representative of the miscible displacing fluidapproaching breakthrough into the protion well means in the model,

(e) continuing at the same flow conditions the miscible displacing fluidinjection into the injection well means of the formation to move theflood front toward the production well means, and

(f) producing petroleum from the production Well means in the formation.

4. The method of claim 3 wherein the displacing fluid injected into theinjection well means of the model is the native petroleum to be producedfrom the formation and the displaced fluid produced from the productionWell means of the model is the displacing fluid to be injected into theformation.

5. A method for determining the input profile of a flood front shape tobe established adjacent injection well means in a formation for theoptimum production of petroleum therefrom by a miscible floodingprocedure employing the injection of a miscible displacing fluid intosaid formation through injection well means for displacement ofpetroleum in the direction of production well means from which petroleumis recovered, the steps comprising:

(a) providing a hydrodynamic reservoir model having functionally thesame Darcy flow system including geometrical similarity anddimensionless numbers, and the same arrangement of well means forinjection and production purposes as the formation,

(b) operating the model with the well means employed in the formationfor injection and production purposes functionally interchanged in thewell means of the model for production and injection purposes,respectively, and with a displacing fluid injected into the injectionwell means to move a displaced fluid toward the production well means,and where the ratio of the viscosity of said displacing fluid to theviscosity of said displaced fluid employed in the model is thereciprocal of the ratio of the viscosity of the miscible displacingfluid to be injected into the formation to the viscosity of the nativepetroleum to be displaceably produced therefrom, and

(c) operating said model until the shape of the flood front in the modelis established at the time representative of the miscible displacingfluid approaching breakthrough into the production well means.

6. The method of claim 5 wherein the displacing fluid injected into theinjection Well means of the model is the native petroleum to be producedfrom the formation and the displaced fluid produced from the productionwell means of the model is the displacing fluid to be injected into theformation.

References Cited UNITED STATES PATENTS 2,867,277 1/ 1959 Weinaug et al.1669 2,994,372 8/1961 Stone 1669 X 3,113,616 12/1963 Dew et al 16693,123,136 3/1964 Sharp 1669 3,139,929 7/1964 Habermann 1669 3,199,5878/1965 Santourian 1669 3,205,943 9/1965 Foulks 1 66--9 OTHER REFERENCESHartsock, J. H. et al., The Effect of Mobility Ratio and VerticalFractures on the Sweep Efliciency of a Five-Spot. In Producers Monthly,September 1961, pp. 37.

Muskat, Morris, Physical Principles of Oil Production. Mc-Graw-Hill, NewYork, 1949, pp. 674, 677, 678.

CHARLES E. OCONNELL, Primary Examiner. JACOB L. NACKENOFF, Examiner.

I. A. CALVERT, Assistant Examiner.

2. A METHOD FOR DETERMINING THE INPUT PROFILE OF A FLOOD FRONT SHAPE TOBE ESTABLISHED ADJACENT INJECTION WELL MEANS IN A FORMATION FOR THEOPTIMUM PRODUCTION OF PETROLEUM THEREFROM BY A MISCIBLE FLOODINGPROCEDURE EMPLOYING THE INJECTION OF A MISCIBCLE DISPLACING FLUID INTOSAID FORMATION THROUGH INJECTION WELL MEANS FOR DISPLACEMENT OFPETROLEUM IN THE DIRECTION OF PRODUCTION WELL MEANS FROM WHICH PETROLEUMIS RECOVERED, THE STEPS COMPRISING: (A) PROVIDING A RESERVOIR MODELHAVING FUNCTIONALLY THE SAME DARCY FLOW SYSTEM INCLUDING GEOMETRICALSIMILARITY AND DIMENSIONLESS NUMBERS, AND THE SAME ARRANGEMENT OF WELLMEANS FOR INJECTION AND PRODUCTION PURPOSES AS THE FORMATION, (B)OPERATING THE MODEL WITH THE WELL MEANS EMPLOYED IN THE FORMATION FORINJECTION AND PRODUCTION PURPOSES FUNCTIONALLY INTERCHANGED IN THE WELLMEANS OF THE MODEL FOR PRODUCTION AND INJECTION PURPOSES, RESPECTIVELY,AND WITH THE RATIO OF THE VISCOSITY OF THE MISCIBLE DISPLACING FLUID TOTHE VISCOSITY OF DISPLACED FLUID AS FUNCTIONALLY EMPLOYED IN THE MODELBEING THE RECIPUROCAL OF THE RATIO OF THE VISCOSITY OF THE MISCIBLEDISPLACING FLUID TO BE INJECTED INTO THE FORMATION TO THE VISCOSITY OFTHE NATIVE PETROLEUM TO BE DISPLACEBALY PRODUCED THEREFROM, AND (C)OPERATING SAID MODEL UNTIL THE SHAPE OF THE FLOOD FRONT IN THE MODEL ISESTABLISHED AT THE TIME REPRESENTATIVE OF THE MISCIBLE DISPLACING FLUIDAPPROACHING BREAKTHROUGH INTO THE PRODUCTION WELL MEANS.